Preheat the oven to 350. Microwave butter and chocolate in a bowl until melted. Add the egg yolk. In another bowl, mix flour, ¾ cup sugar, 1/3 cup cocoa powder, baking powder and salt. Stir in ½ cup milk, vanilla and the butter mixture. Spread into an ungreased, shallow 2 qt. baking dish.
Mix the remaining ½ cup sugar, remaining 1/3 cup cocoa powder and brown sugar in another bowl and sprinkle over batter. Heat the remaining 2 cups of milk until simmering (microwave works) and slowly pour over the mixture in the baking dish (don’t stir). Bake for 40 to 50 minutes-keep an eye on this towards that time because it won’t take long to burn. The top will be a cake/brownie texture so check it with a toothpick, inserted in the center, some moist crumbs should be attached or however you want it to come out…it’s chocolate and hard to go wrong.
Spoon into bowls and add a scoop (or two) of vanilla ice cream on the side. Serve immediately or pudding layer will be absorbed by the cake layer….which really isn’t that heartbreaking because it’s all good.